1. CJM 2013 (vol 66 pp. 284)
 Eikrem, Kjersti Solberg

Random Harmonic Functions in Growth Spaces and Blochtype Spaces
Let $h^\infty_v(\mathbf D)$ and $h^\infty_v(\mathbf B)$ be the spaces
of harmonic functions in the unit disk and multidimensional unit
ball
which admit a twosided radial majorant $v(r)$.
We consider functions $v $ that fulfill a doubling condition. In the
twodimensional case let $u (re^{i\theta},\xi) = \sum_{j=0}^\infty
(a_{j0} \xi_{j0} r^j \cos j\theta +a_{j1} \xi_{j1} r^j \sin j\theta)$
where $\xi =\{\xi_{ji}\}$ is a sequence of random
subnormal variables and $a_{ji}$ are
real; in higher dimensions we consider series of spherical harmonics.
We will obtain conditions on the coefficients $a_{ji} $ which imply
that $u$ is in $h^\infty_v(\mathbf B)$ almost surely.
Our estimate improves previous results by Bennett, Stegenga and
Timoney, and we prove that the estimate is sharp.
The results for growth spaces can easily be applied to Blochtype
spaces, and we obtain a similar characterization for these spaces,
which generalizes results by Anderson, Clunie and Pommerenke and by
Guo and Liu.
Keywords:harmonic functions, random series, growth space, Blochtype space Categories:30B20, 31B05, 30H30, 42B05 

2. CJM 2008 (vol 60 pp. 822)
 Kuwae, Kazuhiro

Maximum Principles for Subharmonic Functions Via Local SemiDirichlet Forms
Maximum principles for subharmonic
functions in the framework of quasiregular local semiDirichlet
forms admitting lower bounds are presented.
As applications, we give
weak and strong maximum principles
for (local) subsolutions of a second order elliptic
differential operator on the domain of Euclidean space under conditions on coefficients,
which partially generalize the results by Stampacchia.
Keywords:positivity preserving form, semiDirichlet form, Dirichlet form, subharmonic functions, superharmonic functions, harmonic functions, weak maximum principle, strong maximum principle, irreducibility, absolute continuity condition Categories:31C25, 35B50, 60J45, 35J, 53C, 58 

3. CJM 2004 (vol 56 pp. 225)
 Blower, Gordon; Ransford, Thomas

Complex Uniform Convexity and Riesz Measure
The norm on a Banach space gives rise to a subharmonic function on the
complex plane for which the distributional Laplacian gives a Riesz measure.
This measure is calculated explicitly here for Lebesgue $L^p$ spaces and the
von~NeumannSchatten trace ideals. Banach spaces that are $q$uniformly
$\PL$convex in the sense of Davis, Garling and TomczakJaegermann are
characterized in terms of the mass distribution of this measure. This gives
a new proof that the trace ideals $c^p$ are $2$uniformly $\PL$convex for
$1\leq p\leq 2$.
Keywords:subharmonic functions, Banach spaces, Schatten trace ideals Categories:46B20, 46L52 

4. CJM 1999 (vol 51 pp. 673)
 Barlow, Martin T.; Bass, Richard F.

Brownian Motion and Harmonic Analysis on Sierpinski Carpets
We consider a class of fractal subsets of $\R^d$ formed in a manner
analogous to the construction of the Sierpinski carpet. We prove a
uniform Harnack inequality for positive harmonic functions; study
the heat equation, and obtain upper and lower bounds on the heat
kernel which are, up to constants, the best possible; construct a
locally isotropic diffusion $X$ and determine its basic properties;
and extend some classical Sobolev and Poincar\'e inequalities to
this setting.
Keywords:Sierpinski carpet, fractal, Hausdorff dimension, spectral dimension, Brownian motion, heat equation, harmonic functions, potentials, reflecting Brownian motion, coupling, Harnack inequality, transition densities, fundamental solutions Categories:60J60, 60B05, 60J35 
